5,668 research outputs found
Stochastic stability versus localization in chaotic dynamical systems
We prove stochastic stability of chaotic maps for a general class of Markov
random perturbations (including singular ones) satisfying some kind of mixing
conditions. One of the consequences of this statement is the proof of Ulam's
conjecture about the approximation of the dynamics of a chaotic system by a
finite state Markov chain. Conditions under which the localization phenomenon
(i.e. stabilization of singular invariant measures) takes place are also
considered. Our main tools are the so called bounded variation approach
combined with the ergodic theorem of Ionescu-Tulcea and Marinescu, and a random
walk argument that we apply to prove the absence of ``traps'' under the action
of random perturbations.Comment: 27 pages, LaTe
Multicomponent dynamical systems: SRB measures and phase transitions
We discuss a notion of phase transitions in multicomponent systems and
clarify relations between deterministic chaotic and stochastic models of this
type of systems. Connections between various definitions of SRB measures are
considered as well.Comment: 13 pages, LaTeX 2
Clues to the nature of dark matter from first galaxies
We use thirty-eight high-resolution simulations of galaxy formation between
redshift 10 and 5 to study the impact of a 3 keV warm dark matter (WDM)
candidate on the high-redshift Universe. We focus our attention on the stellar
mass function and the global star formation rate and consider the consequences
for reionization, namely the neutral hydrogen fraction evolution and the
electron scattering optical depth. We find that three different effects
contribute to differentiate warm and cold dark matter (CDM) predictions: WDM
suppresses the number of haloes with mass less than few M; at
a fixed halo mass, WDM produces fewer stars than CDM; and finally at halo
masses below M, WDM has a larger fraction of dark haloes than
CDM post-reionization. These three effects combine to produce a lower stellar
mass function in WDM for galaxies with stellar masses at and below
M. For , the global star formation density is lower by a
factor of two in the WDM scenario, and for a fixed escape fraction, the
fraction of neutral hydrogen is higher by 0.3 at . This latter
quantity can be partially reconciled with CDM and observations only by
increasing the escape fraction from 23 per cent to 34 per cent. Overall, our
study shows that galaxy formation simulations at high redshift are a key tool
to differentiate between dark matter candidates given a model for baryonic
physics.Comment: 11 pages, 8 figures, submitted to MNRA
Productivity and efficiency of central government departments: a mixed-effect model applied to Dutch data in the period 2012-2019
Central government aims to stimulate the efficiency and technical change of public organizations. However, government primarily focuses on the institutions that deliver final public services, but not on the policy making institutions. This article analyses the productivity of central government departments (CGDs). From bureaucratic theory we hypothesize that productivity of these CGDs are low. In order to measure efficiency and technical change we estimate an average cost function based on data of Dutch individual CGDs during the period 2012-2019. The dataset consists of data on various services provided, resource usage and efficiency determinants. The cost function is estimated by a mixed-effect non-linear least squares method. The outcomes show that there are large efficiency differences among CGDs. It is also striking that technical change of the CGDs is nonexistent over time, probably due to a lack of innovative behaviour, unwieldy bureaucracies and increasingly complex paperwork
NIHAO XX: The impact of the star formation threshold on the cusp-core transformation of cold dark matter haloes
We use cosmological hydrodynamical galaxy formation simulations from the
NIHAO project to investigate the impact of the threshold for star formation on
the response of the dark matter (DM) halo to baryonic processes. The fiducial
NIHAO threshold, , results in strong expansion of the DM
halo in galaxies with stellar masses in the range . We find that lower thresholds such as (as employed
by the EAGLE/APOSTLE and Illustris/AURIGA projects) do not result in
significant halo expansion at any mass scale. Halo expansion driven by
supernova feedback requires significant fluctuations in the local gas fraction
on sub-dynamical times (i.e., < 50 Myr at galaxy half-light radii), which are
themselves caused by variability in the star formation rate. At one per cent of
the virial radius, simulations with have gas fractions of
and variations of , while simulations have order of
magnitude lower gas fractions and hence do not expand the halo. The observed DM
circular velocities of nearby dwarf galaxies are inconsistent with CDM
simulations with and , but in reasonable agreement with .
Star formation rates are more variable for higher , lower galaxy masses, and
when star formation is measured on shorter time scales. For example,
simulations with have up to 0.4 dex higher scatter in specific star
formation rates than simulations with . Thus observationally
constraining the sub-grid model for star formation, and hence the nature of DM,
should be possible in the near future.Comment: 18 pages, 13 figures, accepted to MNRA
Hysteresis phenomenon in deterministic traffic flows
We study phase transitions of a system of particles on the one-dimensional
integer lattice moving with constant acceleration, with a collision law
respecting slower particles. This simple deterministic ``particle-hopping''
traffic flow model being a straightforward generalization to the well known
Nagel-Schreckenberg model covers also a more recent slow-to-start model as a
special case. The model has two distinct ergodic (unmixed) phases with two
critical values. When traffic density is below the lowest critical value, the
steady state of the model corresponds to the ``free-flowing'' (or ``gaseous'')
phase. When the density exceeds the second critical value the model produces
large, persistent, well-defined traffic jams, which correspond to the
``jammed'' (or ``liquid'') phase. Between the two critical values each of these
phases may take place, which can be interpreted as an ``overcooled gas'' phase
when a small perturbation can change drastically gas into liquid. Mathematical
analysis is accomplished in part by the exact derivation of the life-time of
individual traffic jams for a given configuration of particles.Comment: 22 pages, 6 figures, corrected and improved version, to appear in the
Journal of Statistical Physic
Sharp interface limit for a phase field model in structural optimization
We formulate a general shape and topology optimization problem in structural
optimization by using a phase field approach. This problem is considered in
view of well-posedness and we derive optimality conditions. We relate the
diffuse interface problem to a perimeter penalized sharp interface shape
optimization problem in the sense of -convergence of the reduced
objective functional. Additionally, convergence of the equations of the first
variation can be shown. The limit equations can also be derived directly from
the problem in the sharp interface setting. Numerical computations demonstrate
that the approach can be applied for complex structural optimization problems
The edge of galaxy formation III: The effects of warm dark matter on Milky Way satellites and field dwarfs
In this third paper of the series, we investigate the effects of warm dark
matter with a particle mass of on the smallest
galaxies in our Universe. We present a sample of 21 hydrodynamical cosmological
simulations of dwarf galaxies and 20 simulations of satellite-host galaxy
interaction that we performed both in a Cold Dark Matter (CDM) and Warm Dark
Matter (WDM) scenario. In the WDM simulations, we observe a higher critical
mass for the onset of star formation. Structure growth is delayed in WDM, as a
result WDM haloes have a stellar population on average two Gyrs younger than
their CDM counterparts. Nevertheless, despite this delayed star formation, CDM
and WDM galaxies are both able to reproduce the observed scaling relations for
velocity dispersion, stellar mass, size, and metallicity at . WDM
satellite haloes in a Milky Way mass host are more susceptible to tidal
stripping due to their lower concentrations, but their galaxies can even
survive longer than the CDM counterparts if they live in a dark matter halo
with a steeper central slope. In agreement with our previous CDM satellite
study we observe a steepening of the WDM satellites' central dark matter
density slope due to stripping. The difference in the average stellar age for
satellite galaxies, between CDM and WDM, could be used in the future for
disentangling these two models.Comment: 10 pages, 11 figures, accepted for publication on MNRA
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